# Undergraduate Colloquium Spring 2012

Wednesdays at 5:00 p.m. in McHenry Building - Room 4130

Refreshments served at 4:45 p.m.

For further information, please contact

Continuing Lecturer Frank Bauerle, bauerle@ucsc.edu.

**April 11, 2012**

**Games Night**

**Dr. Frank Bauerle Continuing Lecturer, Mathematics Department **

Games nights are an informal get-together of people interested in playing and learning about games with depth that will happen occasionally during the year. Each night will feature a new game or a collection of games. Games can be purely strategic (such as "Hex" or "Ricochet Robots"), involve chance and probability (such as "The game of Pigs" and "Settlers of Catan") or require a certain amount of game psychology (such as "For Sale" or "Pit"). The most interesting games usually combine some or all of the above. Some games are two-player games and some will be for as many players as you can crowd around the game board. We will have fun learning and playing the games but also spend some time discussing the mathematical content of these games. Bring a friend! Bring a new game to share! No prior experience or exposure to any of these games is necessary.

**April 18, 2012**

*On the uniqueness of the projective plane of order 4*

*On the uniqueness of the projective plane of order 4*

**Professor Bruce Cooperstein, UCSC Mathematics Department **

A projective plane is a geometric object consisting of a set P of points and a collection L of special subsets of P, whose elements we call lines which satisfies the following: 1) Two points lie on a unique line. 2) Two lines meet in a unique point. 3) There exists four points no three of which are on the same line (non-colinear). An easy argument implies that all lines have the same cardinality. When this is finite and equal to n+1 we say this is a projective plane of order n. We will give some examples and show that all planes of order 4 are isomorphic.

**April 25, 2012**

**Games Night**

**Dr. Frank Bauerle Continuing Lecturer, Mathematics Department **

Games nights are an informal get-together of people interested in playing and learning about games with depth that will happen occasionally during the year. Each night will feature a new game or a collection of games. Games can be purely strategic (such as "Hex" or "Ricochet Robots"), involve chance and probability (such as "The game of Pigs" and "Settlers of Catan") or require a certain amount of game psychology (such as "For Sale" or "Pit"). The most interesting games usually combine some or all of the above. Some games are two-player games and some will be for as many players as you can crowd around the game board. We will have fun learning and playing the games but also spend some time discussing the mathematical content of these games. Bring a friend! Bring a new game to share! No prior experience or exposure to any of these games is necessary.

**May 2, 2012**

*Resources for Future Mathematics Teachers: Cal Teach & Mathematical Problem Solving*

*Resources for Future Mathematics Teachers: Cal Teach & Mathematical Problem Solving*

**Gretchen Andreasen, Director, CalTeach and Professor Bruce Cooperstein, UCSC Mathematics Department **

Among the resources for future mathematics teachers at UCSC are the Cal Teach K-12 internship program and Math 30, a course in mathematical problem solving that was designed for future teachers. Gretchen Andreasen, the director of Cal Teach, will introduce the paid internships and other resources Cal Teach provides for future math teachers. Professor Bruce Cooperstein will lead a short, fun session of mathematical problem solving to introduce the course, which will be offered in Fall 2012. Deli appetizers will be provided.

**May 9, 2012**

*From triangles to fractions to Riemann's sphere.*

*From triangles to fractions to Riemann's sphere.*

**Professor Richard Montgomery, UCSC Mathematics Department **

A point in the Euclidean plane is specified by a single complex number. We can translate, rotate, and dilate the plane by addition and multiplication by complex numbers. It follows that by applying arithmetic operations to the vertices of a triangle we can form fraction invariant under (oriented) similarities. If we let the triangle degenerate this fraction can have the form z/0 which we call `infinity'. Thus the fractions are best viewed as points in Riemann's sphere. From there we digress to stereographic projection, spherical geometry and cones over spheres.

**May 16, 2012**

**Games Night**

**Dr. Frank Bauerle Continuing Lecturer, Mathematics Department **

Games nights are an informal get-together of people interested in playing and learning about games with depth that will happen occasionally during the year. Each night will feature a new game or a collection of games. Games can be purely strategic (such as "Hex" or "Ricochet Robots"), involve chance and probability (such as "The game of Pigs" and "Settlers of Catan") or require a certain amount of game psychology (such as "For Sale" or "Pit"). The most interesting games usually combine some or all of the above. Some games are two-player games and some will be for as many players as you can crowd around the game board. We will have fun learning and playing the games but also spend some time discussing the mathematical content of these games. Bring a friend! Bring a new game to share! No prior experience or exposure to any of these games is necessary.

**May 23, 2012**

**Movie Night: ***The Proof: A documentary about Andrew Wiles' work on Fermat's Last Theorem*

*The Proof: A documentary about Andrew Wiles' work on Fermat's Last Theorem*

**Dr. Frank Bauerle Continuing Lecturer, Mathematics Department **

For over 350 years, some of the greatest minds of science struggled to prove what was known as Fermat's Last Theorem - the idea that a certain simple equation had no solutions in positive integers. The theorem has gained notoriety in part because of the following published statement by Pierre de Fermat: "It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain." Now hear from the man who spent many years of his life cracking the problem.

**May 30, 2012**

*The Cone over Riemann's sphere and Newton's three-body problem (A self-contained Part 2)*

*The Cone over Riemann's sphere and Newton's three-body problem (A self-contained Part 2)*

**Professor Richard Montgomery, UCSC Mathematics Department **

Richard will review contents from his May 11th talk and add the ingredients of a metric. The key notion is that of the quotient metric, which we apply to obtain a metric on the space of congruence classes of triangles: triples of points in the plane modulo rigid motions. We explain how this yields a `reduced' Newton's equations for encoding three body motions in terms of equations on the cone over Riemann's sphere. Itis not necessary to have heard Part 1 to comprehend Part 2. Notes for the talk can be found here In this talk, Richard will review the contents from his talk on May 11th and go from there. In other words, it is not necessary to have heard Part 1 to comprehend Part 2. Notes for the talk can be found here: http://count.ucsc.edu/~rmont/classes/classes.html